Multiplication principle - practice problems

Number of problems found: 435

Conditional probability
Suppose a batch contains 10 items of which 4 are defective. Two items are drawn at random from the batch one after the other, without replacement. What is the probability that: I) both are defective? Ii) the second item is defective?
A committee
A committee of 6 is chosen from 8 men and 7 women. Find how many committees are possible if a particular man must be included.
Equilateral 75284
Given are 6 line segments with lengths of 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm. How many equilateral triangles can make from them? List all the options.
Overbooking flight
A small regional carrier accepted 12 reservations for a particular flight with 11 seats. 7 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 49% chance, independently
A bag 4
A bag contains 18 balls that differ only in colour, 11 are blue and 7 red. If two balls are picked, one after the other without replacement, find the probability that both are (i) Blue (ii) Of the same colour (iii) Of different colours
Four digit codes
Given the digits 0-7. If repetition is not allowed, how many 4 digit codes that are greater than 2000 and divisible by 4, are possible?
In an
In an square ABCD n interior points are chosen on each of its side. Find the number of all triangles whose vertices X, Y, Z lie at the this points and on different sides of the square.
Indistinguishable 74294
We have eight compartments where we put three indistinguishable balls and two distinguishable ones. How many options do we have?
Probability 73714
I roll six six-sided dice; what is the probability that exactly three threes will fall?
Menu choice
In a Jollibee, you have a menu choice of C1, C2, and C3. For a dessert, you have a choice of ice-cream and mango peach. How many different options do you have?
A bag 2
A bag contains 7 green and 8 red jellybeans. How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 4?
Calculation 73364
From the number 5,4,0,7,8, create three-digit numbers so that they do not repeat and solve the problem by calculation.
Four-digit 73114
How many four-digit numbers can we assemble from the digits 2, 6, 3, 5, 1, and 9 if the numerals in the number cannot be repeated?
T-shirts 73074
Dušan has 8 T-shirts and three pairs of shorts in his closet. How many ways can he dress for school?
Probability 73054
We roll six dice. What is the probability that: a) a six falls twice b) six falls four times
Between 72924
How many ways do we know to select three cards from a deck of seven cards so that there are two red and one green between them?
Probability 72324
We used the digits 2, 3, 4, 5, and 7 when entering the PIN code, and we only used each digit once. What is the probability that someone will guess our PIN code on the first try?
Groups 72194
I have eight groups. How could they place first, second and third?
Three-digit 72184
How many three-digit numbers can be created from the numbers 1, 2, 3, and 4 if you can repeat them?
Probability 71784
What is the probability that if you roll the die twice, the sum of 12 will fall?

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